Honestly I feel both IISc and IISER must take entrance only through their respective entrances and KVPY. Coz JEE is more engineering oriented. I am in no way trying to claim that engineering students are not fit for Science but all I’m saying is people who are taking science or engineering should be segregated into two sections. JEE for engineering KVPY/NEST/IAT for science.

And which website should I visit to know more about the cutoffs for particular branches

No marks are disclosed of any kind. There’s no data anywhere. The best thing you can get is just people already in IISER telling you how much they got in the test. For example, people say that around 100-110 marks in the SCB test fetches IISER Pune.

Also, it’s a science college, there’s no specific branch. You’ll be taught everything and then in the 3rd semester I think, you select your major. @Viraam_Rao